City are battling Manchester United for the England international, 23.
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However, the Mirror says Anderson has let it be known that his priority is to join City this summer, despite United's revvival under manager Michael Carrick.
City are now confident of clinching Anderson's signing and will seek to strike terms of around £65m with Forest for the Geordie.
City want to reach a deal for Anderson before the World Cup so to avoid his price skyrocketing should the midfielder enjoy a big USA campaign.
Anderson has also made it clear he expects to leave the City Ground this summer, even if Forest avoid the drop this season.